# 【CodeChef April Challenge 2014】Final Battle of Chef / 题解

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## 题目描述

Chef declared war on Byteland. Chefs best scientist Pramod has designed a new Fighter Plane which can fly with Speed of Light!! So none of the defence forces of Byteland can defeat or defend it.

Byteland has a structure of a tree with $N$ cities connected by $N-1$ bidirectional roads. Each city has index between $[1,n]$ (inclusive) and no two cities have same index. The capital city of Byteland has index $1$. The distance between two cities is the number of roads in the path from one to other.

If the plane drops a bomb on a city $A$, with damage value $X$ then the damage done to a city $B$ will be $\lfloor \frac{X}{2^d}\rfloor$ where $d$ is the distance between $A$ and $B$, note that as the distance of $A$ from itself is $0$, the damage done to $A$ will be $\lfloor \frac{X}{2^0}\rfloor = X$.

Each city has a certain wealth $W_i$ in it, if it is damaged by a value of $X$ then its wealth is reduced by $X$. On a day if the wealth of a city becomes less than or equal to zero then it is considered Economically Dead.

Your task is to write a program that keeps track of the bombings done by the plane and answer the queries asked by the chef. The chef has a total of $Q$ queries for you. There are two types of queries.

1. Chef gives you two integers $A$ and $X$, which means that the plane drops a bomb on the city with index $A$ with damage value $X$. A bomb can also be dropped on economically dead city.
2. Chef gives you an integer $A$ and you need to print the number of cities that are economically dead which have $A$ in the path from the capital to them.
(See explanation for better understanding)

### Constraints

$1 \leq N \leq 10^5$

$1 \leq Q \leq 10^5$

$1 \leq X \leq 10^5$

$1 \leq W_i \leq 10^9$